HELP! How to repair drywall mud knockdown texture closet wall

last month

I want to remove the builder's grade closet system in a guest closet and install my own. However, the closet isn't normal smooth drywall with paint. It is what I'd call mud/textured. (see attached photos). Doesn't show the whole closet - but just to get an idea of the current closet system and "walls".

How am I supposed to repair all the holes from removal of the builder's grade closet with this type of wall?

Thank you!

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